| Derivative knowledge is an important part for senior students mathematics learning. It is the basic tool to solve the problem of variable for senior students in the future, which lays a foundation for further study, and also has a wide use in daily life. Therefore, how to conduct derivative teaching becomes an important topic to mathematics teachers.Derivative changes maths from static state and the finiteness, into motion, limitless and highly abstract, which makes it hard for students to understand and therefore make mistakes time and again. Previous researches mostly focused on the errors from the perspective of knowledge and the right answer. There were few researching from the cognition angle are few perspective, and to say nothing of researching on teaching strategies to reduce the common mistakes.According to the above situation, based on cognitive learning theory, this paper analyzes the common errors in the implementation of target to avoid wrong teaching strategies.This study focuses on the lectures, through classroom observation, analysis of homework every day and individual interviews of teachers and students to understand the mistakes students often make. On the basis of the preliminary understanding,tests are applied to let the student analyze the reasons for the error after reviewing the standard answer. On this basis, through interviewing the students and checking part of the real meaning of the answers,the students’ real thoughts can be understood so that the cognitive errors can be analyzed more accurately. Based on the analysis of students’ common errors in "derivative and its application" test, the qualitative analysis method is used. Study has confirmed that in the learning process, students are prone to the type of errors as follows:1. Misuse the old concept to solve the problems which are supposed to be solved using new concept;2. Disconnect between the name of the concept and content;3. Wrong use of the formulas and laws;4. The confusion of necessary and sufficient condition in solving the problems of reverse.For the errors in derivative learning students, this study adopts the following teaching methods to avoid or reduce the corresponding common errors, and applies them to the new students in Senior Two:1. The assimilation of the tangent of the old and new concepts (using existing knowledge to create cognitive conflict; promoting the interaction of old and new knowledge, constructing the new system of tangent);2. The close relationship of the concept and the content. Great importance is attached to the formation of the concept of derivative, provide a rich example (through living examples, physical instance, tangent slope a variety of background to promote the understanding of the derivative concept; to establish proper concept of mental representation to promote a comprehensive understanding of the derivative; to practice between the name and content of the concept);3. Memory by Organization and classification, identify formula and rules (using "organization and classification method " to memorize derivation formula and laws; use variable types to identify correct use of formulas and rules);4. Training of reverse thinking, accurate logic cognitive (allocate the difficulties in the monotonicity to develop their ability in a spiral way; inform the training objectives to make the students focus on reverse thinking; summarizes the conclusion of reverse thinking, perfect the cognitive structure; set up corresponding production, improve skills of solving problems effectively;combine training and feedback repeatedly, help students to maintain the correct learning method).According to the comparative study between Senior Three and Senior Two students, conclusions are as follows:in this study students’common errors are often related to his cognitive structure defects. By adopting some teaching strategies to help them form good cognitive structure, teachers can effectively help students correctly extract the knowledge and method, so as to avoid or reduce errors. |
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